The invention relates to adaptive beamforming, and in particular to a closed-loop multistage beamformer.
In this application, the following notation will be used. Bold upper and lower case letters will denote matrices and vectors, respectively. Scalars are italicized. Superscript H denotes conjugate transposition. Expectation is denoted by E{xc2x7}. Other nomenclature is summarized in Table 1
To avoid confusion, Table 2 defines some terminology as it will be used in this application. Applicants are careful to point out the duality between spatial array processing and other related applications. The subsequent presentation will consider only multi-sensor (spatial) array processing; however, it should be understood that the principals of the architecture could easily be employed in these other applications as well.
In general, sensor arrays are capable of rejecting undesirable interference and recovering signals of interest. When the characteristics of the interference are unknown, smart signal processing techniques can be used to xe2x80x9cadaptxe2x80x9d to the interference. This information can then be used to reject the undesired interference. This type of processing is broadly termed xe2x80x9cAdaptive Beam Formingxe2x80x9d (ABF). For over 30 years, different xe2x80x9csmart sensorxe2x80x9d algorithms (and the beamforming hardware required to implement them) have been developed to accomplish this goal. To evaluate these techniques, one typically measures their performance, i.e., their ability to recover signals and suppress interference. One also considers the cost of building suitable array hardware (e.g., receivers and I/O links) and signal processing hardware (e.g., nonadaptive and adaptive filters) as required to implement these algorithms. The goal, of course, is to select techniques that attain a very high level of interference suppression at a low cost.
Oftentimes, sensor arrays are designed to have large apertures, obtaining very high sensitivity levels. Such arrays may be highly digitized (either at the element or subarray levels) to improve performance (e.g., by increasing the dynamic range and/or improving system sensitivity and interference rejection). This high level of digitization results in many xe2x80x9cdegrees of freedomxe2x80x9d (DOFs) that can be used for adaptive beamforming. However, the processing hardware required to exploit these DOFs can be prohibitive.
DOFs can be exploited in a fixed fashion, an adaptive fashion, an instantaneously adaptive fashion, or some combination thereof. Applicants associate the type of DOF exploitation with the degree of flexibility possible within an array processing system at design time. A fixed DOF refers to a DOF that can not be adjusted by the processor in a real-time data-dependent fashion. Fixed DOFs are thus maximally inflexible. An adaptive DOF, as defined here, refers to a DOF that can be under real-time processor control, i.e., it can be controlled in a data-dependent fashion. Adaptive DOFs are thus somewhat flexible. An instantaneously adaptive DOF, on the other hand, refers to an adaptive DOF that is under the direct control of the processor at some given instant. Instantaneously adaptive DOFs are thus maximally flexible. Note that this latter term is introduced specifically to distinguish the operation of the invention from that of other ABFs.
To clarify these methods of DOF exploitation, an analogy is offered. A sensor array is analogous to a black box with a large number of control knobs on the outside. A DOF can be thought of as a single control knob. An operator (the processor) monitors the operation of the black box, and adjusts control knobs as needed. A fixed DOF can be thought of as a control knob that the operator is not permitted to touch. An adaptive DOF can be thought of as a control knob that an operator could move. An instantaneously adaptive DOF can be thought of as a control knob that is actually being manipulated (by the operator) at some given instant. Note that while the number of control knobs may be large, the operator may not be capable of turning them all at once. Hence the number of instantaneously adaptive DOFs may be much lower than the number of adaptive DOFs.
Next, the adaptive beamforming problem can be succinctly stated as follows. Suppose one has a sensor array that produces N digitized channels. As such, there are a total of N DOFs available. A sample vector (a.k.a. snapshot) associated with processing time k is given by the Nxc3x971 column vector, xk. The matrix Xk denotes a Nxc3x97L set of snapshots at this time. The interpretation of xk and Xk will depend on the specific array processing application. For example, in some radar fields xk would be a single snapshot from CPI k, and Xk would be the set of all snapshots from CPI k. These snapshots contain energy from J jammers and noise. The task is to build a filter capable of suppressing this interference while receiving signals from direction "THgr".
There are currently two general classes of ABF techniques that might be used to solve this problem. The first general class of ABF techniques is called Fully Adaptive Beam Forming (Full ABF). Full ABF methods use snapshots from all N DOFs (simultaneously) to adapt to the jamming in this N dimensional space. In this sense, Full ABF works with N instantaneously adaptive DOFs. For representative techniques, see B. Van Veen, xe2x80x9cBeamforming: a versatile approach to spatial filtering,xe2x80x9d IEEE ASSP Magazine, April 1988, section IV-V, incorporated herein by reference.
Full ABF thus requires the hardware to simultaneously collect and process data from all N channels. For many algorithms in this class, processing complexity grows as N3. Thus, for large digitized arrays (i.e., large N), the processing complexity and associated size, weight and power can be quite large. Furthermore, the convergence time of the adaptive algorithm typically increases proportional to N. Thus, for large, highly digitized arrays, a large training interval will be required (this is also quite undesirable). Furthermore, adaptive beamforming is typically proceeded by other processing (e.g., filtering) which might then be performed on all N channels, adding to complexity. Lastly, the adaptive processor itself is often situated in a location that is separated from the array (e.g., below deck on a ship). Thus, Full ABF requires a communication network with enough bandwidth to carry all N channels of the array data to the processor.
With sufficient training data, Full ABF techniques will achieve near optimal performancexe2x80x94albeit at a high cost. Problems occur, however, when sufficient training data is not available, or costs are constrained.
The second general class of ABF techniques attempts to achieve good performance (in restricted environments) and rapid convergence at a greatly reduced cost. These techniques, collectively known as Beamspace Adaptive Beam Forming (Beamspace ABF), achieve this goal by accepting poorer performance in environments with a large number of jammers.
Beamspace ABF begins by mapping the N array channels into Nxe2x80x2 beams prior to adaptive interference rejection, as shown in FIG. 1. In this sense, Beamspace ABF works with only Nxe2x80x2 instantaneously adaptive DOFs (the remaining Nxe2x88x92Nxe2x80x2 DOFs are all fixed DOFs). This mapping is determined by a Nxc3x97Nxe2x80x2 linear transformation matrix, T, which is called the xe2x80x9cbeamspace transformation matrix.xe2x80x9d The beamspace transformation is used to create a set of Nxe2x80x2 xc3x971 beamspace snapshot vectors, Yk, via:
Yk=THXk xe2x80x83xe2x80x83(1) 
(a single such beamspace vector is denoted yk).
Next, adaptive processing is performed with the goal of adapting to the jamming. This processor has access only to the beamspace snapshots. Thus, the adaptation can be viewed as taking place within a Nxe2x80x2 dimensional space. For representative techniques, see B. Van Veen, xe2x80x9cBeamforming: a versatile approach to spatial filtering,xe2x80x9d IEEE ASSP Magazine, April 1988, section VI, incorporated herein by reference. At this stage, the adaptation methods that are employed are analogous to those used in Full ABF. Consequently, the factors described above (adaptation complexity, size, weight, power, convergence rate, availability of training data, and bandwidth) are all functions of Nxe2x80x2 instead of N. As Nxe2x80x2 is usually much less than N, this yields a substantial reduction in required resources.
The price paid for this reduction in resources is performance, especially when the number of important jammers (i.e., jammers radiating powers that exceed the sidelobe suppression of the mainbeam), J, is large. In a radar context, the optimal filter for rejecting the interference in yk is the Wiener filter:
wk=Rkxe2x88x921(THd) 
zk=wkYyk xe2x80x83xe2x80x83(2) 
where
Rk=E{ykykH 
and d is a vector containing the array""s response to a target signal of interest.
As long as Nxe2x80x2 greater than J, the matrix T can be chosen to yield near-optimal interference suppression. However, if Nxe2x80x2xe2x89xa6J one cannot, in general, suppress all interference by merely combining elements of yk.
The apparent implications and drawbacks of this statement are ominous. First, only Nxe2x80x2xe2x88x921 jammers can be completely cancelled. In practice, the actual number of jammers can be expected to vary with time. As a result, the real-time processing hardware must be in-place to support the maximum number of jammers anticipated. All resources required to accommodate this Nxe2x80x2 must be continuously available, even when the current jamming environment does not require them. Because the maximum number of jammers could be very large, only marginal reductions in required resources may be realized as compared with Full ABF.
Second, proper selection of T can be costly. Generally speaking, the best beamspace consists of a set of beams spanning the jamming subspace. This implies prior knowledge about the jamming which, in turn, can be gained by open-loop spectral/parameter estimation applied to the raw channel data. However, these techniques can be costly and/or time consuming. To reduce this cost, it has been proposed that only a subset of elements be used by the open-loop spectral estimator, with superresolution supplying some of the missing resolution. However, this approach is then limited in the rank of the subspace that it can remove (and perhaps also in the accuracy to which the jamming position is known).
The CLM-ABF invention is a method and system for doing adaptive beam forming. In the process of forming these beams, it explicitly tracks source signals (not limited to their angles-of-arrival). In an exemplary embodiment, both functions (i.e., beamforming and tracking) are performed simultaneously. However, it is possible to use the invention in a mode wherein only sources are tracked (i.e., the creation of final beams is turned off).
CLM-ABF processes data from a large digitized array. CLM-ABF begins by using a very simple transformation device to reduce the amount of array data. The resulting transformed data is then adaptively processed to track signals and form beams. It will be appreciated that the initial data reduction is important here because it reduces many costs associated with adaptive processing, i.e., those that increase with the amount of data. This adaptive processor also controls the transformation device, providing additional mitigation of interference. In this sense, CLM-ABF processes only Nxe2x80x2 DOFs in an instantaneously adaptive fashion, with the remaining Nxe2x88x92Nxe2x80x2 DOFs also being adaptive, albeit at a slower rate.
The number of sources that can be tracked and nulled by CLM-ABF depends on the size of the array (i.e., number of sensors) and not upon the amount of data that is actually processed by the second (adaptive) processing stage. That is, the number of xe2x80x9cinstantaneously adaptive DOFsxe2x80x9d does not limit tracking and nulling performance even though the number of instantaneously adaptive DOFs is much smaller than the total number of DOFs).
The built-in source tracking, estimation and stage-1 null steering is done in a closed-loop fashion. As a result, the processor can truly null jammers, i.e., the achievable null depths are similar to those attained by standard adaptive methods (e.g., LMS, or SMI) and not limited due to sensor manifold miscalibration, improper DOF selection, or other error sources.
Accordingly, the invention provides, a system and method of tracking ambient signals, detecting or receiving desired signals, and suppressing undesired signals. An array of sensors receives ambient signals and generates N channels of data. A transformation device accepts the data from the array and generates Nxe2x80x2 channels of data. An adaptive processor accepts the Nxe2x80x2 channels of data from the output of the transformation device and processes the Nxe2x80x2 channels of data to update the settings of the transformation device. Only Nxe2x80x2 degrees of freedom are adaptively manipulated by the adaptive processor at any instant, the manipulation being done in a manner that instantaneously senses changes in signal environment and adjusts the settings of the transformation device in a closed-loop. The adaptive processor optionally combines these Nxe2x80x2 channels to produce system output beam(s) that remove residual interference present out the output of the transformation device. Over time, the adaptive processor controls all N degrees of freedom adaptively, thus nulling and tracking performance is then limited by the N degrees of freedom and not the Nxe2x80x2 degrees of freedom that are actually used adaptively at any instant.